Common pool resource (CPR) dilemmas constitute a class of social dilemmas in which equilibrium behavior results in Pareto deficient outcomes that are not at all desirable by the group. We focus on a class of CPR dilemmas that, in addition to strategic uncertainty about the harvesting behavior of the other group members, include environmental uncertainty about the size of the CPR. In an attempt to decrease the rate of requests from the common pool, and thereby increase individual payoffs, we extend previous research-both theoretically and experimentally-in two different directions. In the bonus treatment, a reward is given to the agent(s) who requests the least, and in the penalty treatment, a charge is imposed on the agent(s) who requests the most. We show that under equilibrium play the bonus treatment decreases total group request, whereas the penalty treatment increases it. Our experimental results do not support this prediction. Rather, both treatments considerably decrease the rate of request and, therefore, increase the rate of provision. The penalty treatment is shown to be more effective in reducing individual requests and enhancing provision rates than the bonus treatment. Copyright 2001 Academic Press.